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We present a data-driven framework based on Lyapunov theory to providestability guarantees for a family of hybrid systems. In particular, we areinterested in the asymptotic stability of switching linear systems whoseswitching sequence is constrained by labeled graphs, namely constrainedswitching linear systems. In order to do so, we provide chance-constrainedbounds on stability guarantees, that can be obtained from a finite number ofnoisy observations.  We first present a method providing stability guarantees from sampledtrajectories in the hybrid state-space of the system. We then study the hardersituation where one only observes the continuous part of the hybrid states. Weshow that in this case, one may still obtain formal chance-constrainedstability guarantees. For this latter result we provide a new upper bound ofgeneral interest, also for model-based stability analysis

Learning stability guarantees for constrained switching linear systems from noisy observations